Text Book on the Method of Least Squares

Text-Book on the Method of Least Squares is one of the foundational English-language treatises on the mathematical theory and practical application of the method of least squares. Written by noted mathematician and engineer Mansfield Merriman this classic volume provides a clear and systematic introduction to the principles used to analyze observations estimate unknown quantities and minimize errors in scientific and engineering measurements. Beginning with the theory of observational errors Merriman explains the concepts of precision accuracy probable error and the laws governing the distribution of errors. The book then develops the method of least squares from first principles demonstrating how the most probable values of unknown quantities may be obtained by minimizing the sum of the squares of residual errors. Through carefully worked examples readers learn how to apply the method to direct observations indirect observations conditioned observations and systems of equations involving multiple unknowns. Although written in the nineteenth century the work remains historically important because the method of least squares continues to be a cornerstone of modern statistics data analysis regression machine learning and scientific modeling. Readers interested in the development of statistical reasoning will find in Merriman’s text a lucid presentation of ideas that later became fundamental to quantitative research across many disciplines. Ideal for students of mathematics statistics engineering astronomy surveying and the history of science Text-Book on the Method of Least Squares offers both a rigorous introduction to error theory and a fascinating window into the evolution of mathematical methods that still underpin modern data analysis.